Question

if log 8 base x + log 8 base 1/ 6 = 1 /3 then the value of x​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=12}}}$

$\pink{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\bold{Given :}$

$log_{8}(x) \times log_{8}( \frac{1}{6} ) = \frac{1}{3} \\ ⇛ log(x) \times \frac{1}{6} = \frac{1}{3}$

$\bold\red{According\:to\:logarithmic\:law}$

$log_{a}(m) + log_{a}(n) = log_{a}(nm) \\ ⇛ log_{8}( \frac{x}{6} ) = \frac{1}{3} \\ ⇛ \frac{x}{6} = {8}^{ \frac{1}{3} }$

Since,

$if \: \: log_{a}( N) = x \: ⇛N = {a}^{x} \\ ⇛x = 6 \times {( {2}^{3} )}^{ \frac{1}{3} } \\ ⇛x = 6 \times 2 \\ ⇛x = 12$

Answer 2

Step-by-step explanation:

log 8/ logx + log8/ log ⅙ =1/3

log 8/log x - log 8/ log 6 =1/3

log6- logx / logx log6=1/3log8